For the time being, there is no change to the daily operations at Dolce Vita, Wiles said.

"We are not in any hurry. But if someone pays asking price, we will sell," Wiles said.

Wiles, who also owns Montrose's Vinoteca Poscol and the acclaimed Da Marco Cucina E Vino, said he has no plans to shutter his other two restaurants.

"Absolutely not. Da Marco will be 20 years-old in March 2020. It's my baby," Wiles said. "And Poscol has a great following."

As well, Wiles has no plans to add to his restaurant holdings. "We're trying to take a step back. That would be going in the wrong direction," he said.

Dolce Vita, which opened in January 2006, is known for its superb Neapolitan-style wood-fired pizza, antipasti and pastas.

"Regulars obsess over the shaved raw Brussels sprouts with Pecorino cheese; the flash-fried rapini; the simple spaghetti with clams," wrote Alison Cook as she named the restaurant to her 2018 Top 100 Houston Restaurant list.

"My own obsession is with the frighteningly perfect pizza Margherita, with its vibrant tomato, twinge of fresh basil and silky, stretchy pools of buffalo mozzarella."